Details

analyze1.4s (11%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
25%	74.9%	0.1%	8
54.6%	45.2%	0.1%	9
56.2%	43.7%	0.1%	10
62.4%	37.4%	0.1%	11
65.9%	33.9%	0.1%	12
66.3%	33.5%	0.1%	13
69%	30.8%	0.1%	14

Compiler

Compiled 17 to 15 computations (11.8% saved)

sample150.0ms (1.2%)

Algorithm

1×

intervals

Results

106.0ms	143×	body	1024	valid
22.0ms	46×	body	512	valid
6.0ms	21×	body	256	valid
6.0ms	46×	body	128	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify175.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5170	26

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

4.2b

Counts

2 → 1

Compiler

Compiled 32 to 28 computations (12.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
0.2b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
3.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite42.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64_78`
34×	`add-sqr-sqrt_binary64_100`
30×	`associate-l_binary64_19`
26×	`times-frac_binary64_84`
25×	`add-cube-cbrt_binary64_113`
21×	`sqrt-prod_binary64_94`
14×	`unpow-prod-down_binary64_157`
11×	`add-exp-log_binary64_116`
9×	`add-cbrt-cube_binary64_114` `pow1_binary64_139`
8×	`distribute-lft-out_binary64_29`
6×	`pow-unpow_binary64_155`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95`
3×	`associate-r_binary64_18` `unswap-sqr_binary64_46`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip-+_binary64_52` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-pow_binary64_150` `associate-/r/_binary64_24` `flip3-+_binary64_81`
1×	`-commutative_binary64_9` `sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `rem-sqrt-square_binary64_91` `div-inv_binary64_75` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `pow1/2_binary64_158`

Counts

4 → 103

Calls

4 calls:

18.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(pow.f64 (sin.f64 kx) 2)
3.0ms	(pow.f64 (sin.f64 ky) 2)

series344.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

223.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
87.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
19.0ms	(pow.f64 (sin.f64 ky) 2)
14.0ms	(pow.f64 (sin.f64 kx) 2)

simplify62.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5006	2288

prune175.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	105	10	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	10	116

Error

3.1b

Counts

116 → 10

Compiler

Compiled 2949 to 1657 computations (43.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 ky) 2)
0.5b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
3.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite67.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

104×	`sqrt-prod_binary64_94`
60×	`add-sqr-sqrt_binary64_100`
50×	`*-un-lft-identity_binary64_78`
34×	`sqrt-pow1_binary64_96`
30×	`pow1_binary64_139`
28×	`sqrt-div_binary64_95`
20×	`add-cube-cbrt_binary64_113`
19×	`swap-sqr_binary64_45`
18×	`pow1/2_binary64_158`
15×	`unpow-prod-down_binary64_157`
14×	`distribute-lft-out_binary64_29`
11×	`associate-l_binary64_19` `associate-r_binary64_18`
10×	`rem-sqrt-square_binary64_91`
9×	`pow-prod-up_binary64_148` `unswap-sqr_binary64_46`
8×	`flip-+_binary64_52` `flip3-+_binary64_81`
7×	`add-exp-log_binary64_116`
6×	`add-cbrt-cube_binary64_114`
5×	`pow-sqr_binary64_51` `pow-prod-down_binary64_149`
4×	`sqr-abs_binary64_93` `add-log-exp_binary64_117` `frac-times_binary64_88`
3×	`pow-unpow_binary64_155`
2×	`associate-l/_binary64_21` `associate-r/_binary64_20`
1×	`pow2_binary64_159` `*-commutative_binary64_9` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `unpow2_binary64_143` `sqr-pow_binary64_50` `sqrt-unprod_binary64_98` `pow-pow_binary64_150` `rem-square-sqrt_binary64_90` `pow-plus_binary64_141`

Counts

4 → 147

Calls

4 calls:

27.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(pow.f64 (sin.f64 ky) 2)

series287.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

98.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
88.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
86.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
14.0ms	(pow.f64 (sin.f64 ky) 2)

simplify109.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4970	3097
1	4970	3097

prune251.0ms (2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	159	10	169

Error

3.1b

Counts

169 → 10

Compiler

Compiled 4935 to 2999 computations (39.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
1.8b	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
3.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite97.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

101×	`sqrt-prod_binary64_94`
87×	`*-un-lft-identity_binary64_78`
66×	`times-frac_binary64_84`
53×	`add-sqr-sqrt_binary64_100`
51×	`add-cube-cbrt_binary64_113`
45×	`add-exp-log_binary64_116`
39×	`associate-l_binary64_19`
27×	`add-cbrt-cube_binary64_114`
20×	`prod-exp_binary64_127`
18×	`unpow-prod-down_binary64_157` `distribute-lft-out_binary64_29`
12×	`sqrt-div_binary64_95`
11×	`div-exp_binary64_129` `associate-/r*_binary64_22` `pow1_binary64_139`
10×	`cbrt-unprod_binary64_111`
6×	`cbrt-undiv_binary64_112`
4×	`add-log-exp_binary64_117` `flip-+_binary64_52` `associate-/r/_binary64_24` `flip3-+_binary64_81`
3×	`1-exp_binary64_122` `associate-/l_binary64_23` `rec-exp_binary64_128` `pow-prod-down_binary64_149` `associate-r/_binary64_20`
2×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `div-inv_binary64_75` `pow1/2_binary64_158`
1×	`-commutative_binary64_9` `frac-2neg_binary64_89` `frac-times_binary64_88` `associate-r_binary64_18` `associate-l/_binary64_21` `clear-num_binary64_77`

Counts

4 → 166

Calls

4 calls:

36.0ms	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
13.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
10.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series620.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

233.0ms	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
212.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
88.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
85.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify122.0ms (1%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4931	5592
1	4931	5592

prune342.0ms (2.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	173	5	178
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	175	13	188

Error

3.1b

Counts

188 → 13

Compiler

Compiled 6804 to 4292 computations (36.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
1.7b	(/.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
3.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite79.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

88×	`sqrt-prod_binary64_94`
68×	`*-un-lft-identity_binary64_78`
44×	`times-frac_binary64_84`
38×	`add-sqr-sqrt_binary64_100`
36×	`add-cube-cbrt_binary64_113`
22×	`associate-/r*_binary64_22`
16×	`unpow-prod-down_binary64_157` `distribute-lft-out_binary64_29`
15×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
12×	`sqrt-div_binary64_95`
6×	`pow1_binary64_139`
5×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
4×	`add-log-exp_binary64_117` `flip-+_binary64_52` `associate-/l*_binary64_23` `associate-/r/_binary64_24` `flip3-+_binary64_81`
2×	`sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `rem-sqrt-square_binary64_91` `frac-2neg_binary64_89` `div-inv_binary64_75` `clear-num_binary64_77` `pow1/2_binary64_158`
1×	`associate-*r/_binary64_20` `associate-/l/_binary64_25`

Counts

4 → 137

Calls

4 calls:

28.0ms	(/.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
17.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series621.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

228.0ms	(/.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
210.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
93.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
89.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify89.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4944	4737
1	4944	4737

prune274.0ms (2.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	146	3	149
Fresh	3	8	11
Picked	1	0	1
Done	0	1	1
Total	150	12	162

Error

3.1b

Counts

162 → 12

Compiler

Compiled 5301 to 3162 computations (40.4% saved)

regimes1.0s (8.1%)

Accuracy

Total 1.3b remaining (32.9%)

Threshold costs 0b (0%)

Compiler

Compiled 12747 to 10078 computations (20.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	26
1	16	26

end0.0ms (0%)

sample6.2s (49.3%)

Algorithm

1×

intervals

Results

3.5s	4671×	body	1024	valid
663.0ms	1357×	body	512	valid
192.0ms	1409×	body	128	valid
173.0ms	543×	body	256	valid
27.0ms	20×	body	2048	valid

Compiler

Compiled 1440 to 1140 computations (20.8% saved)

Details

analyze1.4s (11%)

sample150.0ms (1.2%)

simplify175.0ms (1.4%)

prune3.0ms (0%)

localize18.0ms (0.1%)

rewrite42.0ms (0.3%)

series344.0ms (2.7%)

simplify62.0ms (0.5%)

prune175.0ms (1.4%)

localize18.0ms (0.1%)

rewrite67.0ms (0.5%)

series287.0ms (2.3%)

simplify109.0ms (0.9%)

prune251.0ms (2%)

localize18.0ms (0.1%)

rewrite97.0ms (0.8%)

series620.0ms (4.9%)

simplify122.0ms (1%)

prune342.0ms (2.7%)

localize16.0ms (0.1%)

rewrite79.0ms (0.6%)

series621.0ms (4.9%)

simplify89.0ms (0.7%)

prune274.0ms (2.2%)

regimes1.0s (8.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample6.2s (49.3%)

Profiling